Waveplates or rotators (the terms “rotators” and “waveplates” are used interchangeably herein) have been used extensively in optics in order to manipulate a signal's state of polarization. For instance, waveplates are often used to rotate the direction of polarization of an incident optical signal. One specific type of waveplate is the half-wave plate. The half-wave plate rotates an incident polarization state 90°. Another type of waveplate is the quarter-wave plate. The quarter-wave plate converts linearly polarized light into circularly polarized light.
A waveplate includes an optical material or waveguide that exhibits birefringence. A birefringent material or waveguide is one having an effective refractive index that depends on the polarization direction of the optical signal. The birefringent material or waveguide is said to have two principle axes, often called a slow and a fast axis, referring to the axis that have maximum and minimum refractive index respectively.
In order to manipulate the state of polarization, the waveplate is inserted in the optical path, such that an input portion of the optical path (input path) supplies the optical signal to the waveplate and an output portion of the optical path (output path) receives the optical signal from the waveplate. The waveplate's axes are oriented at some angle with respect to the angle of the incident light, or to the principle axis of the input path, which may include a waveguide. The length of the waveplate, along with orientation thereof, will determine the function that the waveplate serves. In many applications, the waveplate will have an orientation of 45° with respect to the principle axis of the input and output paths.
A waveplate may be inserted or fabricated between the input and output paths, or sections. The input and output sections could be waveguides or free space for instance. Likewise the waveplate can be a slab of material or a waveguide structure. The input and output sections could include the same or different waveguide types or materials. If they are different, relatively short identical sections may be inserted in front of, and after, the waveplate. The input and output sections are assumed to have principle axes defined as TE (transverse electric) and TM (transverse magnetic). TE and TM typically refer to the orientations in planar optics where TE is the orientation parallel to the substrate and TM is the orientation perpendicular to the substrate. In free space TE and TM could be replaced by the S and P orientations, which are orientations relative to the laboratory frame. The waveplate has principle axis labeled P1 and P2, where P1 is oriented by angle θ with respect to the TE axis. In many applications, it is desirable for the angle θ to be 45°. P1 and P2 are mutually orthogonal, as are TE and TM. An incident signal excites some portion of P1 and P2, and, due to the birefringence, the signal portions on P1 and P2 travel with different phase velocities. At the output of the waveplate, P1 and P2 excite modes TE and TM. The excitation is a phasor and vector sum of P1 and P2. The angle θ and the length of the waveplate are chosen to achieve some specific functionality relating the input polarization and the output polarization of the optical signal propagating through the waveplate or rotator.
An example of a conventional free space (or slab) waveplate may include a slab of material having two principle axes P1 and P2 which exhibit birefringence, and in which the orientations of P1 and P2 are different than those of the principle axis of the input and outputs paths.
In planar optics, slab waveplates may be incorporated by cutting a slot through the waveguide and then inserting the waveplate. Alternatively, waveplates can be fabricated by modifying the structure of the waveguide along desired sections.
A conventional waveguide may have a rectangular cross section and principle modes that are TE and TM oriented. More generally, waveguides that have some mirror symmetry plane (such as left-right symmetry) will also support TE and TM oriented principle modes. In order to create principle modes that have an orientation tilted with respect to the TE and TM axis an asymmetry may be incorporated into the waveplate or waveguide. Asymmetries might also be induced by changing the refractive index throughout the waveguide or cladding. Asymmetries can create new principle states with orientations tilted with respect to the TE and TM orientations of other conventional symmetric waveguides in a planar optical circuit.
As noted above, a half-wave plate is used to rotate the polarization of an incident signal by 90°. Such a rotator is often referred to as a polarization converter because it converts the incident polarization state into the orthogonal state. For example, in planar waveguides, the TE (or TM) state is converted to a TM (or TE) state. In free space the S (or P) state is converted to a P (or S) state. Typically, a half-wave plate is configured to have the principle axis of the waveplate oriented 45° with respect to the incident signal. For instance, in planar waveguides, the P1 or P2 axis or eigen mode of the waveplate is oriented at 45° with respect to the TE and TM axis or eigen mode of the input and output paths, as shown in FIG. 1. (Note that P1 and P2 are mutually orthogonal, and TE and TM are mutually orthogonal). Further, in the ideal half-wave plate, the length of the plate is chosen such that the cumulated phase difference between the P1 and P2 states accumulates to a phase φ.
Mathematically, the cumulated differential phase difference, φ, between the two polarization eigen states or eigen modes of a waveplate or rotator is:
                    ϕ        =                                            2              ⁢              π                        λ                    ⁢                      L            ⁡                          (                                                NP                  ⁢                                                                          ⁢                  1                                -                                  NP                  ⁢                                                                          ⁢                  2                                            )                                                          eq        ⁢                                  ⁢                  (          1          )                    
Where λ is the wavelength, L is the plate length, and NP1, NP2 are the effective indexes of the P1 and P2 eigen states, respectively. For a half-wave plate, the L is chosen so that φ=π.
In practice, perturbations affect the ideal half-wave plate. For instance, the tilt angle of P1 with respect to TE as shown in FIG. 1 may not be exactly 45°. This is especially prevalent in planar waveguides fabricated waveplates. Random fabrication deviations can lead to deviations D about the target of 45° (see FIG. 1). These deviations lead to deterioration in the performance of the optical circuit or device including the rotator or waveplate.
The performance degradation of a conventional (single-stage) half-wave plate is depicted in the curve or response 200 shown in FIG. 2. The x-axis measures the deviation away from an ideal 45° tilt (measured in degrees), and the y-axis measures the polarization extinction ratio in decibels. The extinction ratio is the ratio of power in the unwanted polarization at the output, to the input power. For instance, if the input signal has a TE orientation, then the output should be a pure TM signal for an ideal half-wave plate. Perturbations or deviations in the tilt of 45° result in some of the output signal remaining in the TE orientation. The extinction ratio is then the power in the TE orientation at the output compared to the net TE power at the input. As shown in FIG. 2, response 200 is highly peaked, implying that small deviations in the input optical signal away from ideal (45°) lead to poor extinction ratio.
Accordingly, a rotator or waveplate is desired that is more tolerant of deviations in an input optical signal polarization away from a desired orientation.